Firstly, I am an intern at a software company. My supervisor is off today and tomorrow, but I've run out of things to do. I'm happy to just code away on my own thing to improve, but I do not wish to have trouble later on with my supervisor due to this and seem like I am lazy or a bad employee.
I thought about asking the person above him (a director) for something to do, however, I have emailed him yesterday already mentioning a project he never got back to me about and never got a reply. I feel like this is a sign that there is really nothing that he has for me today, especially since this sort of void period has happened previously. I don't wish to be seen as pushy and put a director on pressure to find me something to do, especially when he is busy with something else.
Is it better to talk to him, or just practice and learn coding as I await the return of my supervisor?